Sets, Relations & Functions
Subsets with Even Product and n(B)≥2
nta_pyq_2026_jan
Grade 11
Question:
Let $S$ be the set of the first 11 natural numbers. Then the number of elements in $A=\{B\subseteq S:n(B)\geq2\text{ and the product of all elements of }B\text{ is even}\}$ is _____.
Step-by-Step Solution
Key Concept: Product is even $\Leftrightarrow$ at least one even element. Count complements: subsets with odd product = all elements odd. Odd elements in $S$: $\{1,3,5,7,9,11\}$ (6 elements). Subsets of odd elements with $n(B)\geq2$: $2^6-7=57$.
1979.
Correct Answer: 1979